The present invention relates to a method of analysing crystalline texture.
A wide range of materials have a crystalline structure and these include minerals, ceramics, semi-conductors, superconductors, metals and alloys. The vast majority of these materials are polycrystalline, that is composed from a number of component crystals which are often referred to individually as xe2x80x9cgrainsxe2x80x9d.
The crystallographic orientations of the crystals in a polycrystalline sample relative to a fixed reference are seldom random. Where there is some preferred orientation of the crystals then the material is said to exhibit a xe2x80x9ctexturexe2x80x9d. Crystalline planes and directions are conventionally represented using Miller indices with {hkl} representing the crystal planes in terms of the normal to the crystal planes, and  less than uvw greater than  representing the crystal directions within these {hkl} planes. The texture of a sample can therefore be represented by relating these crystalline planes and directions to corresponding physical directions with respect to the sample.
Conventionally a crystalline texture in a plate or thin film sample is represented as {hkl} less than uvw greater than . These planes and directions are parallel to two corresponding orthogonal directions in the sample. In general this is arranged such that {hkl} represents the crystal plane normals which are parallel to the plane normal of the sample, known as the xe2x80x9cnormal directionxe2x80x9d (ND), and  less than uvw greater than  represents the crystalline directions within these planes that are parallel to a xe2x80x9clongitudinalxe2x80x9d or xe2x80x9crolling directionxe2x80x9d (RD) within the sample. The samples are therefore prepared such that RD lies within the plane of the sample and ND is perpendicular to RD, and normal to the sample surface.
Crystalline texture is important in materials science as a number of material properties are dependent upon the orientations of the crystals. For example, silicon steels have directions of high magnetic permeability along their  less than 100 greater than  crystal directions, a fact which is used in the production of transformer cores.
Traditionally the representation of textures in polycrystalline materials has been carried out using pole figure (PF) or Euler angle methods.
A pole figure can be regarded as a scatter plot showing how the respective crystals are oriented relative to an external frame of reference such as that of the sample. A specific direction with respect to the crystal structure is selected, and for each crystal in the sample this direction is plotted as a point on a stereographic projection (showing the intersection of the direction with a surrounding sphere).
The pole figure therefore represents a statistical distribution of a particular crystal direction, for all grains in which the crystallographic orientation is measured and plotted. The pole figure can be obtained by grain-by-grain measurements or collectively by polycrystalline diffraction using x-rays.
There are a number of problems associated with the use of pole figures. One of these is that the appearance of the pole figure is dependent upon the particular crystal direction plotted, due to the crystal symmetry. Considerable expertise and experience in crystallography is required to interpret pole figures, particularly as even a specific texture will have a different appearance depending upon the crystal direction that is plotted in the pole figure.
A further problem is that many of the points within the pole figure are actually related by the crystal symmetry and this makes the interpretation of the pole figures difficult because consideration of the crystal symmetry is also required.
When more than one texture is present within a sample, these textures are superimposed in the pole figures which makes their individual identification problematical. Whereas some common textures in simple crystal systems may be recognisable by an expert, pole figures showing more complicated textures such as those with large index values for {hkl} and/or  less than uvw greater than , or for less common crystal systems are much more difficult to interpret.
An alternative to pole figures is to use the Euler method in which consideration is made of the rotations to each crystal that would be required in order to bring each crystal into alignment with a particular orientation in the sample. The crystal orientations relative to the sample can be represented by three consecutive rotations (Euler angles) around selected orthogonal axes attached to the crystal.
These angles are represented as three rotations around orthogonal axes and each individual measurement of the crystal orientation in the sample is plotted as a point located in the resultant three dimensional xe2x80x9cEuler anglexe2x80x9d space. Using this method, the existence of texture will be marked by clusters of points in the space. As the space is three dimensional, this is usually displayed by a series of slices cut along one of the axes.
In a similar manner to the pole figure method, crystal symmetry makes interpretation of the Euler plot extremely difficult to visualise and understand, particularly with multiple or complicated textures and uncommon crystal systems.
There is therefore a need to simplify crystalline texture analysis such that crystalline texture information can be more readily obtained and interpreted without the high levels of skill and experience often required in known methods.
In accordance with a first aspect of the present invention we provide a method of analysing crystalline texture from data defining the orientation of crystals in a sample of polycrystalline material, the method comprising:
for each crystal, determining the orientation of a first direction in the sample, with respect to a common reference frame fixed to the crystal structure of each crystal;
selecting a number of crystals sharing a similar orientation of the first direction with respect to the reference frame;
for each selected crystal, determining the orientation of a second direction in the sample with respect to the reference frame;
selecting a number of crystals sharing a similar orientation of the second direction with respect to the reference frame; and
determining and/or representing a crystal texture corresponding to the orientation of the selected crystals with respect to the first and second directions within the sample.
One advantage of the present invention is that it provides a method in which crystal texture can be determined and/or represented in such a manner that it is more easily interpreted. This is enabled by the use of a reference frame attached to the crystal structure rather than to the sample, and the determination of the orientations of first and second directions in the sample with respect to the crystals. Those crystals sharing a common orientation with respect to the sample are therefore selected and the texture may be represented and/or determined accordingly.
The method also enables the automation of the steps of determining the orientation of the crystals with respect to the crystal structure and indeed their selection. This can be performed by a suitably programmed computer.
Preferably the first and second directions are orthogonal, thereby allowing these directions to be related to the directions used by convention in describing crystalline texture.
Although the analysis of the crystal texture could be performed by computation, preferably the orientation of the first and/or second direction with respect to the reference frame, is displayed to a user of the system as an inverse pole figure (IPF). Typically separate IPFs are used for the first direction and second direction.
The use of the common reference frame is convenient for the purposes of presentation to the user in that, unlike the pole figure method, the information displayed is not dependent upon the pre-selection of a particular crystallographic direction. However, the first and second directions are chosen to define the orientation of the sample. Typically one of the first or second directions are arranged to be the rolling direction or longitudinal direction of the sample (RD) with the other corresponding direction being the normal direction of the sample (ND).
The use of inverse pole figures (IPF) is also particularly advantageous in that, due to crystallographic symmetry, rather than using a full stereographic projection, a unit triangle of the IPF projection can be selected as this represents all of the information within the IPF. Preferably therefore the inverse pole figures are displayed as unit triangles, the advantage being that crystallographically equivalent points are superimposed at the same position within the unit triangle of the IPF.
Unlike in prior methods, common directions within the crystals including equivalent directions related by symmetry, can therefore be represented as single points in the IPFs which greatly reduces confusion in their interpretation.
Using the data describing the orientation of each crystal in the sample, the orientation of a crystal is represented by the position of a data point in each of the IPFs for the first and second directions. Each data point in the IPF represents a measurement taken at a particular location on the sample although typically multiple measurements are made on a sample and plotted accordingly.
The data points in the IPFs may also be represented using colored regions reflecting the data point density as this density is indicative of crystal texture.
High density regions can be located automatically by analysis of the data, although preferably these are located visually in the IPFs by a user. Typically in either case, a region of high data density is selected and a point chosen within this region. An angular range about the point is defined and if necessary, the position of the point is adjusted until all points within the high density cluster are within this angular range. A crystal plane (including those related by symmetry) {hkl} equivalent to the point is then calculated. The angular range is chosen to account for experimental error in the data. Preferably an angle of less than 15 degrees is used. A similar angle is used in data selection in the IPFs for the normal direction and the rolling direction. Although data points of either the normal direction (ND) or the rolling direction (RD) can be selected first, preferably the IPF corresponding to the normal direction (ND) is used to select the first region.
Upon selection of such a region within a first IPF, in general only the data corresponding to the region within the defined angular range of the chosen point are then used in plotting the second IPF.
The selected data are typically used to plot corresponding data describing the orientation of the associated crystals with respect to the rolling direction (RD) in the form of the second IPF.
One or more crystal textures can be identified in the second IPF by locating high densities of data points. As crystal directions in a texture lie within a plane having an associated plane normal, preferably by defining the direction of the plane normal using the IPF for ND, the corresponding crystal directions can be searched for in the IPF for RD. This is subject to the constraint that the ND and RD directions are orthogonal (within experimental errors). If the selection is performed under the control of a user then typically the computer restricts the selection of the data to data points in accordance with this orthogonality limitation.
Following conversion of the selected RD IPF data into a crystal direction (and those related by symmetry)  less than uvw greater than  Using the center of mass model, the data are preferably output as a texture in the form of crystallographic planes and directions, {hkl} less than uvw greater than .
This process may be repeated a number of times for different regions of high data point density in the first and the second IPF in order to determine multiple textures present within the sample. These identified textures can be output as data or represented graphically for example by coloring crystals in an image according to their determined texture.
The method is not limited to crystals of a particular material phase and therefore multiple phase or multiple component materials can also be analysed and the texture determined for each.
The data defining the orientation of the crystals is generally obtained from diffraction and therefore the method preferably further comprises initially obtaining diffraction patterns from a number of the crystals in the sample. Typically electron diffraction patterns are obtained from each crystal, for example using a transmission electron microscope or scanning electron microscope. However electron back-scattered diffraction is preferably used as this provides a convenient method of obtaining a diffraction pattern from each of the crystals within the sample.
Automated analysis of these electron diffraction patterns, in conjunction with data describing the crystal structure, allows the orientation of the crystals to be determined and stored for later analysis. The crystal structure data is typically in the form of data describing lattice parameters, lattice types, point and space groups and atomic occupancies, and is stored in a database. Data can be generated for this purpose for each of the various crystal systems found in nature.
In order to improve visualization of crystal orientations in relation to sample topography and morphology, the method preferably further comprises obtaining an image of the sample, for example using a scanning electron microscope. Sometimes this image can be analyzed using image analysis methods to identify the separate crystals within a sample. When grain boundaries are not visible on such an image, crystal orientation data can be obtained on a fine grid of sample positions and changes in orientation used to determine grain boundaries. Alternatively, the individual orientations measured at each grid point can be color coded so that individual grains become visible as connected areas of similar color.
In one example, the image is processed so that only crystals with orientation corresponding to a particular texture are displayed within the image.
In accordance with a second aspect of the present invention we provide apparatus for analysing crystalline texture from data defining the orientation of crystals in a sample of polycrystalline material, comprising:
a store for containing data defining the orientation of crystals, and
a processor arranged to perform the method according to the first aspect of the invention.
Preferably the apparatus is in the form of a computer such as a PC. This may be the same computer used to control an SEM in order to determine the orientation data such that the apparatus provides unified crystal imaging and texture analysis facility. The apparatus will preferably therefore also include means for determining the data defining the orientation of the crystals, such as an electron microscope, and preferably a scanning electron microscope (SEM) arranged to obtain electron back scattered diffraction (EBSD) patterns.
The apparatus also preferably further comprises a display for presenting to a user with determined orientations of the crystals with respect to the reference frame. This allows the presentation of the texture information to a user as well as possibly an image of the sample. Typically the apparatus will further comprise a selection device such as a keyboard or mouse to enable a user to select a number of the crystals when their orientations are presented on the display.